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Institut de Recerca en Economia Aplicada Regional i Pública Document de Treball 2019/11 1/48 pág.
Research Institute of Applied Economics Working Paper 2019/11 1/48 pág.
“Re-examining the debt-growth nexus: A grouped fixed-effect approach”
Inmaculada Martínez-Zarzoso, Marta Gómez-Puig and Simón Sosvilla-
Rivero
4
WEBSITE: www.ub.edu/irea/ • CONTACT: irea@ub.edu
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Abstract
This paper uses panel data for 116 countries over the period 1995-2016 to
investigate the heterogeneity of the debt-growth nexus across countries and
the factors underlying it. In the first step, the grouped fixed effects (GFE)
estimator proposed by Bonhomme and Manresa (2015) is used to classify
countries into groups, with group membership being endogenously
determined. In the second step, a multinomial logit model is used to explore
the drivers of the heterogeneity detected, among them the quality of
institutions, the composition of debt-funded public expenditure, the relative
public and private indebtedness, and the maturity of debt. Finally, the
underlying factors explaining the time-varying impact of public debt on
growth in the country groups identified is also investigated.
JEL classification: C23, F33, H63, O47, O52.
Keywords: Public debt; economic growth; heterogeneity; grouped fixed-effects; debt-growth link;
panel data; multinomial logit regression.
Inmaculada Martínez-Zarzoso: Faculty of Economic Sciences, University of Göttingen, Germany and Department of Economics, University Jaume I, Castellón. Spain. Email: martinei@eco.uji.es Marta Gómez-Puig: Department of Economics and Riskcenter, Universidad de Barcelona. Email: marta.gomezpuig@ub.edu Simón Sosvilla-Rivero: Complutense Institute for Economic Analysis, Universidad Complutense de Madrid. Email: sosvilla@ccee.ucm.es Acknowledgements
The authors are very grateful to Angel Valarezo-Unda for his assistance with the research and to Julián Andrada-Félix
and Eduardo Acosta-González for their useful suggestions.
1
1. Introduction
The nexus between public debt and economic growth, a traditional focus of study for
economists, has recently undergone a notable revival fuelled by the substantial
deterioration of public finances in many economies after the global financial and economic
crisis of 2008-2009. According to Fitch Ratings, government debt hit $66 trillion through
the end of 2018, or about 80% of global GDP1.
A decade after the global financial crisis, government debt-to-GDP ratios are still above
their pre-crisis levels. These high levels of public sector indebtedness involve risks
especially for advanced and emerging economies. On the one hand, as global monetary
conditions tighten, the debt burden may grow and rollover risks increase. On the other
hand, the debt burden limits the ability of governments to provide support to the economy
in the event of a downturn or a financial crisis. Although there is widespread agreement
about the potentially adverse consequences of unparalleled levels of public debt for
economies’ growth, few macroeconomic policy debates have generated as much
controversy as the austerity argument [see Guajardo et al. (2014), Jordà and Taylor (2016)
or Alesina et al. (2019a, 2019b)], especially in the current context of waning momentum in
the major economies.
From an empirical point of view, the existing literature has grouped studies into two
strands (see Mitze and Matz, 2015). The “first generation” strand includes the works by
Reinhart and Rogoff (2010), Pattillo et al., (2011), Lof and Malinen (2014) and Woo and
Kumar (2015), among others. This strand focused mainly on the nonlinear effects in the
debt-growth relationship and predicted an inverted U-shape relationship between the two
variables (debt begins to harm economic growth when the debt-to-GDP ratio exceeds a
certain threshold – 90%, according to the seminal paper by Reinhart and Rogoff (2010)).
The “second generation” strand goes beyond the nonlinearities in the relationship and
focuses instead on the heterogeneity of debt-growth nexuses across countries [Ghosh et al.
(2013), Pescatori et al. (2014), Edberhardt and Presbitero (2015), Markus and Rainer (2016),
Chudik et al. (2017), Chiu and Lee (2017) or Gómez-Puig and Sosvilla-Rivero (2017,
2018a)]. The studies in the second strand acknowledge that the effects of public debt on
1 The Global Debt Database published by the International Monetary Fund (IMF) shows similar figures. According to
the IMF, global debt has reached an all-time high of $184 trillion in nominal terms, the equivalent of 225% of GDP in 2017. However, of the global total of $184 trillion in debt at the end of 2017, close to two-thirds was nonfinancial private debt and the remaining one-third was public debt.
2
growth may vary depending on country-specific macroeconomic, financial, and institutional
variables.
In this context, the current paper belongs to the above-mentioned “second generation” of
studies and aims to contribute to the existing literature in three respects. First, the
originality of the analysis arises from the adoption of a recently developed method from
the panel time series literature: the grouped fixed effects (GFE) estimator proposed by
Bonhomme and Manresa (2015). To the best of our knowledge, this is the first paper to
apply the GFE methodology to examine whether the debt-growth relationship differs
across groups of countries, with the pattern of heterogeneity being endogenously
determined by the data2. Second, the GFE methodology will also be used to examine
whether the impact of debt on economic growth changes over time by estimating group-
specific time-varying coefficients. Although it is also widely agreed that heterogeneities in
the debt-growth relationship occur not only across countries but also over time, this issue
has hardly been studied by the literature (the exceptions include Yang and Su (2018) and
Gómez-Puig and Sosvilla-Rivero (2018b))3. The third contribution of this paper is to
analyse the drivers of the heterogeneous impact of debt on economic growth. To this end,
we first explore the determinants of group membership, making use of a multinomial logit
regression model to assess the role of five types of variables4: (1) the quality of institutions,
(2) the composition of public expenditure that is funded with debt, (3) relative public
indebtedness, (4) relative private indebtedness, and (5) the maturity of debt5. We then
analyse the role of these variables in explaining the time-varying impact of public debt on
growth in the country groups identified.
2 The GFE estimator takes into account the possibility that different countries experience distinct dynamics in the debt-growth relationship, with the group-specific time patterns and individual group membership being left unrestricted and estimated from the data. Furthermore, the GFE estimator arguably deals better with endogeneity due to unobserved heterogeneity. 3 Yang and Su (2018) extend the regression kink model of Hansen (2017) and find clear evidence that the debt-to-GDP threshold is time-varying and state-dependent (however, a limitation of their work is that the choice of debt-threshold determinants is arbitrary). While Gómez-Puig and Sosvilla-Rivero (2018b) empirically investigate the short and the long run impact of public debt on economic growth by applying the Autoregressive Distributed Lag (ARDL) bounds testing approach. 4 In a recent paper, Fatás et al. (2019) point out that treating debt as a black box and imposing the restriction that any given level of debt has the same consequence on economic growth, regardless of its structure, is simplistic. In particular, they state that one of the reasons why it is difficult to identify common patterns and to pin down the causal effect of debt on growth is that not all debts are equal, and factors such as (1) what the debt was used for, (2) who holds government debt, (3) its currency composition, and (4) its maturity are key elements that can affect fiscal vulnerabilities and the possible reactions of government and private agents to future changes in debt. We tried to find data for the four variables, but obtained data only for the first (what the debt was used for) and the fourth (debt maturity) factors mentioned. Nevertheless, we have also included variables that proxy the quality of the institutions and the relative ratio of both private and public debt. 5 As a proxy for the maturity of debt, we use short-term debt, expressed as a percentage of total external debt.
3
This paper aims to fill these gaps in the literature by focusing on a sample of 116 countries
(advanced, emerging and developing countries) over the period 1995-2016. The main
results show that the relationship between public debt and growth varies across countries.
In particular, the GFE estimator endogenously splits the sample into seven groups of
countries that have dissimilar time patterns and a different estimated impact of a debt
change on economic growth (ranging between -0.43 and -0.031). When analysing the
heterogeneous time-varying impact of public debt on growth, our results indicate that the
debt-growth relationship is crucially mitigated by the quality of a country’s institutions and
intensified by the level of both public and private indebtedness and the maturity of debt.
The type of expenditure that is funded with debt also influences that relationship
(negatively in the case of unproductive spending, and positively in the case of productive
spending).
The rest of the paper is organized as follows. Section 2 presents the rationale for our
empirical approach on the basis of the results of some preliminary descriptive analyses.
Section 3 introduces the analytical framework. Section 4 describes the data used in the
analysis. The econometric methodology is explained in Section 5. Empirical results are
presented in Section 6, while Section 7 explores the determinants of group membership
and the time-varying impact of public debt on growth. Finally, some concluding remarks
and policy implications are offered in Section 8.
2. Descriptive analysis
In what follows, we provide some descriptive analyses highlighting the cross-country
heterogeneity in the evolution of sovereign debt-to-GDP ratio in the 116 countries in our
sample (see Appendix 1) over the period 1995-2016. Figure 1 shows the evolution of the
average debt ratio in the three groups of countries into which the sample can be split,
following the International Monetary Fund (IMF) classification: advanced economies (AE),
emerging market economies (EM), and low income developing countries (LIDC).
[Insert Figure 1 here]
We can observe that, from the outbreak of the global financial crisis (2008-09) until the end
of the sample period in 2016, on average, global general government debt has risen by over
20% of GDP in advanced economies and by around 13% of GDP in emerging markets,
reaching a post-war high [see Bredenkamp et al., 2019 and Yared (2019)], whilst in low-
4
income developing countries (with only a few exceptions) new debt accumulation was
contained during the crisis, thanks largely to the debt relief efforts of the late-1990s and
early 2000s6 (see Eichengreen et al., 2019) and did not experience an increase until 2012 (on
average, 14% of GDP). These increases have given rise to average public debt-to-GDP
ratios of around 75%, 54%, and 56% in advanced economies, emerging markets and
developing countries respectively at the end of 2016.
However, as public debt increases are far from being homogeneous within the three groups
of countries, the debt-to-GDP ratios are highly dispersed in the different groups over the
sample period. More specifically, despite their relatively moderate average values at the end
of 2016, debt-to-GDP ratios registered values above 100% in eight advanced economies
and above 90% in three. Moreover, two emerging market and four low-income developing
countries were also above 100%.
Japan registered the highest government debt (not only in our sample, but also in the
world) at 236% of its GDP in 2016 (although, notably, Japan is also one of the world’s
largest economies and its share of public debt held by non-residents is traditionally very low
– around 5-7% – which reduces its vulnerability). It is followed by Greece, which is still
recovering from the effects of its economic crisis and subsequent bailout, at 183%. It is
noticeable that five euro area countries also registered ratios above or close to 100% at the
end of 2016: Italy, Portugal, Belgium, Spain and France, with figures of 132%, 130%,
106%, 99% and 97% respectively. Finally, several Caribbean and African countries also had
high national debts at the end of the sample period, including Barbados (149%), Jamaica
(114%), Belize (96%), Republic of Congo (129%), Cape Verde (128%), Mauritania (100%),
Sudan (100%) and Egypt (97%).
Of the world’s major economic powers, the United States registered the highest national
debt at 107% of its GDP in 2016. China, the world’s second-largest economy and home to
the world’s largest population, had a public debt ratio of just 44% of its GDP at the end of
20167. Germany, Europe’s largest economy, also had a relatively low sovereign debt ratio at
68%. Among the 116 countries in our sample, at the other end of the scale, Estonia
registered the lowest sovereign-debt-to-GDP ratio in 2016 (9%), followed by three sub-
6 The Heavily Indebted Poor Countries (HIPC) initiative and the associated Multilateral Debt Relief Initiative (MDRI) explain these figures since recipient countries were required to establish a track-record of strong policy performance under IMF and World Bank supported programs before receiving large write-downs of both official bilateral and multilateral debt. 7 However, it is noticeable that China alone accounts for almost three-quarters of the increase in global private nonfinancial debt since the onset of the Global Financial Crisis, which represents over 200% of its GDP (see Bredenkamp et al., 2019)
5
Saharan African countries: Botswana (16%), Congo Democratic Republic (19%) and
Nigeria (20%).
All in all, the above figures indicate that the evolution of the public ratio of indebtedness
presents very different patterns – not only across the 116 countries in our sample, but also
within the three groups into which the sample is divided according to the IMF income-
based classification. This suggests that the use of the GFE methodology, which leaves
group membership unrestricted rather than imposing it ex-ante, may represent a more useful
tool for capturing those heterogeneities8. Moreover, they also provide a good reason for
examining whether the differences in the relationship between debt and economic growth
depend on factors others than per capita income, such as the institutional environment, the
composition of debt-funded public expenditure, the relative ratio of private and public
indebtedness, or debt maturity.
3. Analytical framework
Following Gómez-Puig and Sosvilla-Rivero (2017 and 2018a), the initial empirical
specification is derived from the neoclassical growth model of Solow augmented with
public debt, where the growth rate of real per capita GDP for a given country i in time t (gti)
is given by:
1
1
n
it it ij ijt it it
j
g y X d
(1)
where yit-1 is the logarithm of initial real per capita GDP (to capture the “catch-up effect” or
conditional convergence of the economy to its steady state), Xijt (j=1, …, n) is a set of
control variables, dti is the public debt-to-GDP ratio, and it denotes the error term.
Regarding Xit, we consider a set of explanatory variables that have been shown to be
consistently associated with growth in the literature9: population growth rate as a
8 Gómez-Puig and Sosvilla-Rivero (2017 and 2018a) examined the heterogeneity in the public debt-economic growth nexus in EMU countries by means of time-series techniques. In principle, in those papers they are able to analyse each country separately by allowing complete individual heterogeneity, but this approach is not entirely practical, for several reasons: (1) individual estimations may be rather inefficient since they do not make use of cross-section information and (2) examining countries separately fails to capture any common patterns. On the other hand, much of the previous literature relies on panel data techniques and obtains an average relationship for a given group of countries. Therefore, since it is very important not only to impose some structure on individual heterogeneity but also to allow for different relationships within the sample, the grouped fixed effect (GFE) estimator seems well suited for the purposes of this paper. 9 See Aghion and Howitt (2009) for a comprehensive account of the most important contributions and debates on growth.
6
percentage (POPGRit); the ratio of gross capital formation to GDP (GCFit); life expectancy
at birth, a proxy for the level of human capital (HKit)10; openness to trade, measured by the
sum of exports and imports over GDP (OPENit); and the GDP deflator inflation rate, a
measure of macroeconomic instability and uncertainty (INFit).
In the economic growth literature, the rate of growth of labour used in the production
process and the accumulation of physical capital (investment) are the key determinants of
growth (Solow (1956) or Frankel (1962)). Therefore, population growth (POPGRt) and the
ratio of gross fixed capital formation to real GDP (GCFt) are used to proxy country size
and the rate of labour growth and the accumulation of the physical capital stock
respectively.
A proxy of human capital (HKt) is included to reflect the notion that countries with an
abundance of human capital are more likely to be able to attract investors, absorb ideas
from the rest of the world, and engage in innovation activities (Grossman and Helpman,
1991) Trade openness (OPENt) is posited to boost productivity through transfers of
knowledge and efficiency gains (Seghezza and Baldwin, 2008). Finally, with regard to the
inflation rate (INFt), it has been argued that inflation is a good macroeconomic indicator of
how the government manages the economy [see Fischer (1993) or Barro (2003), among
other authors] and that low inflation brings about economic efficiency because, through the
price mechanism, economies are able to allocate scarce resources to their best economic
use (World Bank, 1990).
4. Data
We use annual data for 116 countries (advanced economies, emerging market economies
and low-income developing countries) over the period 1995-2016 (see Appendix 1).
To maintain as much homogeneity as possible for a sample of 116 countries over the
course of two decades, we use the World Bank’s World Development Indicators as our
primary source. We then strengthen our data with the use of supplementary information
from the International Monetary Fund (International Financial Statistics and World
Economic Outlook, October 2018). As mentioned above, we first use per capita GDP at
2010 market prices, population growth rate, the ratio of gross capital formation to GDP, an
index of human capital, openness to trade and GDP deflator inflation to examine the
10 This proxy is also used by Sachs and Warner (1997).
7
impact of debt on economic growth. The precise definitions and sources of the variables
are presented in Appendix 2. In the second step, we make use of variables that measure the
quality of institutions, the composition of public expenditure, the relative ratio of both
public and private indebtedness, and debt maturity as potential drivers of the relationship
in the different groups of countries found.
With regard to the variables that measure the quality of institutions, in this paper we rely on
the definition of economic institutions proposed by Acemoglu et al. (2005b) where
economic institutions are identified with the structure of property rights and access to
economic resources. Thus, good economic institutions are ones that provide security of
property rights and relatively equal access to economic resources to a broad cross-section
of society. However, measuring the quality of institutions is a challenging task. It is
common practice in the literature to measure it in terms of perceptions, which may not
necessarily reflect the quality of the law but rather the actual workings of the economy. So,
in this paper, to capture differences in the quality of country governance, we adopt a
comprehensive composite index, the World Bank’s Worldwide Governance Indicator
(WGI), which offers better time-variate characteristics than other governance measures.
The WGI index covers six broad dimensions of governance for over 200 countries since
1996, and summarizes views on the quality of country governance provided by a number of
survey organizations, non-governmental organizations, commercial business information
providers, and public sector organizations worldwide. It follows the methodology of
Kaufmann et al. (2010) and is published annually by the World Bank. The six governance
indicators it contains are: (1) voice and accountability, (2) political stability and absence of
violence, (3) government effectiveness, (4) regulatory quality, (5) rule of law, and (6) control
of corruption. This paper focuses on the average of the last four of these indicators11,
which captures the quality of economic and administrative institutions (the definition of
each of the four indicators included in our average measure is presented in Appendix 3). In
particular, these indicators try to capture how the economic structure is able to deliver a
level-playing field for all economic actors, ensure that rent extraction and waste of
resources is limited, and provide sound economic incentives for encouraging people to
invest, innovate, save, solve problems of collective actions and provide public goods.
Therefore, in each year (following Chong and Gradstein (2007) and Beltratti and Stulz
11 Following Helliwell et al. (2014) the six composite measures reported by the World Bank are divided into two groups and only the average of the second group of indicators (which contains four measures primarily concerned with the quality of the delivery of government services: government effectiveness, regulatory quality, rule of law, and the control of corruption) is included in our analysis. The first group of two indicators measures the state of democracy and other aspects of the electoral process (voice and accountability, and political stability and absence of violence).
8
(2012)), we take the simple average of the four components of the WGI presented in
Appendix 3 for each country. We then rescale this raw score so that it lies between zero
and one by subtracting the minimum score from it and dividing the result by the maximum
score minus the minimum score (this variable is named “government quality indicator”
(GQIt) in our analysis).
Data regarding private debt (PRDEBTt) have been drawn from the Global Debt Database.
This database offers the total gross debt of the (private and public) nonfinancial sector for
an unbalanced panel of 190 countries (see Mbaye et al., 2018) and for the 116 countries of
our sample we have selected the variable total private debt as a percentage of GDP. This
variable is calculated as the sum of two components12: (1) bank loans to domestic
households and nonfinancial corporations, drawn from the IMF’s Standardized Reporting
Forms (SRFs) and International Financial Statistics (IFS) and (2) the outstanding stock of
debt securities issued (on the domestic and international markets) by non-financial
corporations, calculated based on securities issuance data from Dealogic database13. Then,
as explained in Appendix 3, much as the World Bank classifies countries by income (see
Fantom and Serajuddi, 2016), we have classified them as low indebted, lower middle
indebted, upper middle indebted, and high indebted, the cut-off points between each of the
groups being the first, the second and the third quartiles. To this end, we use yearly data to
create two dummy variables representing our proxies of the relative public and private
indebtedness: (DQPDt) and (DQPRDt), respectively. These dummy variables take values
from 1 to 4, corresponding to the low indebted, lower middle indebted, upper middle
indebted, and high indebted categories using public14 and private debt-to-GDP ratios
respectively.
With regard to the debt maturity variable, we use short-term debt (STDt), expressed as
percentage of total external debt, as a proxy. Data have been obtained from the World
Bank’s World Development Indicators and from the Coordinated Portfolio Investment
Survey (CPIS) database provided by the IMF.
Finally, the International Monetary Fund Government Financial Statistics was the source
used to collect data regarding government expenditure by purpose. This dataset is usually
known as the classification of the functions of government (COFOG) and divides
12 However, it does not include cross-border bank loans from the Bank for International Settlements dataset because they were not available for all the countries in our sample. 13 Outstanding debt securities are calculated on the basis of maturity at issuance. 14 Public debt-to-GDP data source has already been explained in Appendix 2.
9
government expenditure into 10 categories: (GF01) on general public services, (GF02) on
defence, (GF03) on public order and safety, (GF04) on economic affairs, (GF05) on
environment protection, (GF06) on housing and community amenities, (GF07) on health,
(GF08) on recreation, culture and religion, (GF09) on education, and (GF10) on social
protection. A more detailed overview of the items included in each category is presented in
Appendix 415.
To produce a data matrix without missing values, we apply two complementary
procedures:
the technique of multiple imputation developed by King et al. (2001) (which permits the
approximation of missing data and allows us to obtain better estimates) and the
simultaneous nearest-neighbour predictors proposed by Fernandez-Rodriguez et al. 1999)
(which infers omitted values from patterns detected in other simultaneous time series).
5. Econometric Methodology
Given the relatively small sample available, we use panel data econometrics to combine the
power of cross section averaging with all the subtleties of temporal dependence (see
Baltagi, 2008)16. Indeed, this methodology has already been extensively used in the
literature.
5.1. Time series properties
Since the appropriate econometric treatment of a model depends crucially on the pattern of
stationarity and non-stationarity of the variables under study, before carrying out the
estimation we perform a variety of unit root tests in panel datasets. Specifically, we use the
Levin–Lin–Chu (2002), Harris–Tzavalis (1999), Breitung (2000), Im–Pesaran–Shin (2003),
and Fisher-type (Choi, 2001) tests. The results of these tests17 decisively reject the null
hypothesis of a unit root for git, INFit, POPGRit and GCFit (indicating that they are
stationary in levels, i. e., I(0)), while they do not reject the null for yit, dit, OPENit and HKit
(suggesting that these variables can be treated as first-difference stationary, i. e., I(1))
5.2. Empirical model
15 In each country, expenditure in the different groups is presented as a percentage of GDP. 16The main advantages over single cross-sections or time series data are the following: a) a more accurate inference of model parameters, b) a greater capacity for capturing the complexity of economic relationships, c) more informative results, d) a greater ability to control for individual unobserved heterogeneity, and e) its simpler computation and statistical inference. See Hsiao (2003) for an analysis of the advantages and limitations of using panel datasets. 17 The results of the tests are available upon request from the authors.
10
Given that our dependent variable is stationary (i.e., its statistical properties such as mean,
variance, autocorrelation, etc., remain constant over time), we cannot explain it with non-
stationary variables (whose statistical properties change over time). Additionally, if the
variables in the regression model are not stationary, then the standard assumptions for
asymptotic analysis will not be valid and we cannot undertake hypothesis tests about the
regression parameters. Therefore, by differentiating the non-stationary variables we
transform them into stationary variables.
As a result of the time series properties of our data, the baseline empirical model is as
follows:
1 1 2 3 4 5it i it it it it it it it itg g INF HK OPEN POPGR GCF d (2)
where denotes the first difference operator.
Note that model (2) is quite different from model (1), which is commonly used in the
literature, especially regarding the variables yit-1, HKit, OPENit and dit, since we find that they
are non-stationary and therefore enter our model in first differences. As argued in
Asimakopoulos and Karavias (2016), by rewriting equation (1) as (3)
1
1 1
l ls s ns ns
it i it ij ijt ij ijt it t
j j
g y X X d
(3)
(where s
ijtX and ns
ijtX denote the stationary and non-stationary explanatory variables
respectively), we can compare (3) with our equation (2), which has 1 1it itg y instead of
1ity , itd instead of itd and ns
ijtX instead of ns
ijtX as explanatory variables due to non-
stationarity. The interpretation of the estimated parameters is the same in both models, but
that of , 2 , 3 and changes.
To estimate model (2), we initially consider two basic panel regression methods. The first
one is the pooled-OLS and is based on the following assumptions about unobserved terms:
i is uncorrelated with :itx ( ) 0it iE x
1( , , , , , , )it it it it it it it itx g INF HK OPEN POPGR GCF d
( ) 0it itE x ( itx predetermined)
In this first estimation method, the data for different countries are pooled together and the
equation is estimated by ordinary least squares (OLS).
11
The second method is the fixed-effects (FE) method, based on the following assumptions
about unobserved terms ( i and it ):
i is freely correlated with
1( , , , , , , )it it it it it it it itx g INF HK OPEN POPGR GCF d
( ) 0it isE x for s=1, …,T (strict exogeneity)
Therefore, this second estimation method accounts for differences between countries and
the constant terms i are allowed to vary between them. These constant terms stand for all
unobserved aspects that distinguish the countries from each other (i. e., they capture
country heterogeneity).
5.3. Exploring the possibility of heterogeneous effects
However, the originality of the analysis presented in this paper does not arise from the use
of panel data techniques, but from exploring the possibility of heterogeneous effects of
debt variations on economic growth, accounting for both varying and unvarying
heterogeneity between countries using a recently developed method from the panel time
series literature: the Grouped Fixed Effect (GFE) approach, proposed by Bonhomme and
Manresa (2015)18. The GFE estimator relaxes the strict assumption that all countries follow
the same time trend, and requires only that all countries within a group follow the same
time pattern over time. Nevertheless, the GFE estimator restricts the pattern to being the
same for all countries within a group, but allows different groups to have fully distinct time
patterns.
In contrast to the country fixed effects estimator, the GFE estimator can control for
unobservable time-varying country characteristics that follow a group-specific time pattern.
The main identifying assumption is that the number of distinct country-specific time
patterns of unobserved heterogeneity is equal to the number of groups. In other words, all
countries have to follow one of the group specific time-varying paths of unobserved
heterogeneity.
An additional important feature of the GFE estimator is that group membership of the
countries in our sample is not pre-determined, but is estimated according to a least-squares
18 This estimator has been used in Grunewald et al. (2017) to investigate the relationship between inequality and carbon dioxide emissions and by Oberlander et al. (2017) to assess the distinct effects of social globalization and trade openness on national trends in markers of diet quality.
12
criterion. Countries whose time profiles of the outcome variable (growth rate of real per
capita GDP) – net of the effect of covariates – are most similar are grouped together.
Assume that the countries in our sample are categorized in a number of groups indexed by
j = 1, …, J. The number of groups J must be small compared to the number of countries.
Finally, a further advantage of the GFE estimator is that the time-varying GFE are better
suited to deal with endogeneity in the presence of time-varying unobserved heterogeneity.
In this case, our regression equation takes the following specification:
1 1 2 3 4 5 iit it it it it it it it j t itg g INF HK OPEN POPGR GCF d (4)
where ij t denotes the group-specific time fixed effect which includes group fixed effects
as well as time fixed effects. The estimator is described in detail in Appendix 5.
6. Empirical Results19
Table 1 shows the estimation results using the OLS, panel FE and GFE methodologies. It
can be seen that the growth rate of real per capita GDP is negatively associated with
changes in the public debt-to-GDP ratio. Compared to OLS and FE specifications, the
coefficient of changes in the public debt-to-GDP ratio shrinks slightly in magnitude in the
GFE estimation, but remains statistically significant. An additional point on the public
debt-to-GDP ratio is associated with a reduction in the growth rate by 0.072. A one
standard deviation increase (8.93) in the public debt-to-GDP ratio reduces the rate of
growth by about 0.64 on average, equivalent to a decrease of about 29%20.
It is noticeable that the fit of the overall regressions significantly increases from 0.265 for
the OLS and FE specifications to 0.544 for the GFE. Note also that the values of the
objective function (the Bayesian information criterion, BIC) of the GFE estimation is
lower than the values of the objective function of the OLS and fixed effects estimation,
suggesting that some cross-country heterogeneity is time-varying in our sample and
justifying the appropriate use of the GFE estimator.
[Insert Table 1 here]
19 In each model, we focus our comments on the variation in public debt in order to investigate its effect on growth, summarizing the results by pointing out the main regularities. The reader should browse through Tables 1 and 3 for a detailed account of the impact of other explanatory variables on the growth rate. 20 The mean rate of growth during the sample period is 2.24, being 0.64 the 29% of it.
13
The GFE model uses seven groups (the number being selected using information on the
change in the criterion function). The estimated classification of the countries belonging to
each group is shown in Table 2 and Figure 2.
[Insert Table 2 and Figure 2 here]
Next, in order to investigate whether variations in the public debt-to-GDP ratio have a
different effect on the rate of growth in different groups, we estimated a new model that
allows for specific slopes by including interactions of the variable itd with the group
indicator variables. Table 3 presents the impact of changes in debt-to-GDP ratio on real
per capita GDP growth for the seven detected groups in the sample21.
[Insert Table 3 here]
It can be observed that the coefficient of the interaction term is negative and significant for
all groups and that the estimated impact ranges between -0.43 in Group 1 to -0.031 in
Group 722.
Group 1 and Group 2, the ones with the highest effect of a debt change on economic
growth (-0.43 and -0.23 respectively) are composed entirely by advanced and emerging
market economies: four post-Soviet states in the case of Group 1 −three Baltic states,
Estonia, Latvia and Lithuania, which are now advanced economies and members of the
European Economic and Monetary Union (EMU) and one Eastern Europe country which
is an emerging market economy (Ukraine)−; and five East Asia & Pacific countries, one
European and one sub-Saharan African country in the case of Group 2. Of these, two are
advanced economies (Republic of Korea and Singapore) and five emerging market
economies (Indonesia, Malaysia, Thailand, Russia23 and Botswana). A common
characteristic of countries that belong to Groups 1 and 2 is that they present low or
moderate levels of public debt-to-GDP throughout the sample. The only exception is
Singapore, with an average ratio above 90% throughout the period.
The estimated impact of a debt change on economic growth declines noticeably in Group 3
(-0.14), which includes 16 countries: two post-Soviet states from Eastern Europe,
21 For expository convenience, we have named the endogenously identified groups according to their estimated impact, being Group 1 the one with the highest estimated impact and Group 7 the one with the lowest estimated impact. 22 These results imply that a one standard deviation increase on the public debt-to-GDP ratio reduces the rate of growth by about 60% in Group 1 while the same increase generates only a 10% decrease in Group 7. 23 Russia is one of the EM economies that now issues almost all its debt in local currency. While this shift has reduced currency risk, it has also fostered an increase in the share of debt held by non-residents (who are traditionally more volatile)
14
Moldova24 a low-income developing country and Belarus, an emerging market economy;
four European countries, three of them considered emerging markets (Turkey, Bulgaria
and Romania, the last two are members of the European Union) and one advanced
economy that is a member of the EMU (Slovak Republic); nine Latin American countries
(Brazil, Argentina, Chile, Colombia, Ecuador, Honduras, Panama, Paraguay and Peru)
which are considered emerging economies by the IMF with the exception of Honduras (a
low-income developing country); and one sub-Saharan African country (Namibia) which is
also an emerging market economy. With the exception of Brazil, all of them also present
moderate levels of public debt during the sample period25.
Group 4 and Group 5 present lower impacts (-0.11 and -0.09 respectively) and mainly
include advanced and emerging market economies (though there are also some low-income
developing countries), but the average ratios of both public and private debt are much
higher26. Specifically, Group 4 comprises three advanced economies that belong to the
EMU (Ireland27, Luxembourg and Malta); one Latin American country (Dominican
Republic), an emerging market economy, and two sub-Saharan African countries
(Seychelles, an emerging market country and Cape Verde a low-income developing
country). Group 5, with 40 countries, is the largest, followed by Group 7 with 31 countries
– 21 European countries (12 advanced economies that belong to the EMU: Austria,
Belgium, Cyprus, Finland, France, Germany, Greece, Italy, the Netherlands, Portugal,
Slovenia and Spain; six EU countries outside the currency union: the Czech Republic,
Denmark, Sweden, the United Kingdom, advanced economies, and Croatia and Hungary,
emerging market economies; and three other European advanced economies that do not
belong to the EU: Iceland, Norway and Switzerland; two advanced North American
economies (Canada and the United States); three East Asia and Pacific countries (Japan and
New Zealand, advanced economies, and Fiji , an emerging market economy); eight Latin
American and Caribbean countries (the Bahamas, Barbados, Belize, El Salvador, Jamaica
and Mexico, emerging markets, and Nicaragua and Haiti, low-income developing
24 Fraud in Moldova’s banking system led to a large government bailout in 2014. 25 However, Brazil made a shift to issue its debt in local currency, which has reduced currency risk. Conversely, in Argentina, despite having a lower level of public debt, indebtedness may represent a risk since it is mainly external and can lead to a balance of payments or a currency crisis. Indeed, Argentina has recently experienced significant capital outflows (a similar crisis took place in Turkey, which is also in Group 3). 26The average debt ratio of 100% is surpassed by one country in Group 4 (Seychelles) and by six in Group 5 (Japan, Mauritania, Greece, Jamaica, Italy and Belgium); whilst the ratio of 80% is surpassed by one country in Group 4 (Cape Verde) and by five in group 5 (Barbados, Belize, Canada, Comoros, and Portugal). 27 In Ireland (jointly with Luxembourg and Malta), the effect of a debt change on economic growth is higher than in most of the euro area countries (the majority belong to Group 5). The fact that exposure to foreign creditors is traditionally very high in Ireland (more than 40%) and that a major banking crisis led to a government bailout in 2010 (the debt-to-GDP ratio surpassed 100% between 2011 and 2014 ) might partially explain this difference.
15
countries); three Middle East and North African countries (Israel, Algeria and Iran), the
first being an advanced economy and the other two emerging markets belonging to the
Organization of the Petroleum Exporting Countries (OPEC); and three sub-Saharan
African countries (South Africa28, an emerging market, and Comoros and Mauritania low-
income developing countries).
Finally, in Groups 6 and 7 the estimated effect of a debt change on economic growth
registers the lowest values (-0.04 and -0.03 respectively). They are composed entirely of
emerging markets and low-income developing countries with somewhat more moderate
debt levels, especially in Group 7. More specifically, Group 6 comprises 12 countries, and
some of them with high public debt ratios29: eight sub-Saharan African countries (Congo
Republic, Congo Democratic Republic, Côte d’Ivoire, the Gambia, Madagascar, Mali,
Niger and Gabon) that with the exception of Gabon (an emerging market and member of
OPEC) are low-income developing countries; three Middle East and North African
countries (Morocco, Oman and Saudi Arabia – emerging markets and, in the case of the
last two, oil exporters (Saudi Arabia also belongs to OPEC) and one South Asia low-
income developing country (Nepal). Group 7, the second-largest with 31 countries,
includes30: 14 sub-Saharan African countries (Burkina Faso, Cameroon, Ghana, Guinea,
Kenya, Malawi, Nigeria, Rwanda, Sudan, Tanzania, Uganda, Eswatini, Mauritius, and
Senegal) which are low-income developing countries (oil exporters in the case of Sudan and
Nigeria, which is also an OPEC member) with the exception of the last three, which are
emerging markets; four Middle East and North African countries (Bahrain, Egypt, Jordan
and Tunisia) which are emerging markets (Egypt being an oil exporter); five Latin
American and Caribbean countries (Bolivia, Costa Rica, Guatemala, Uruguay and Guyana)
which are emerging markets with the exception of Guyana (a low-income developing
country); three South Asian countries (India, Pakistan and Sri Lanka); two East Asia and
Pacific countries (China and Philippines) which are also emerging markets; and, finally,
28 South Africa, and to a lesser extent Mexico are also among the EMs countries that made a shift in their debt structure to local currency. 29 This is the case of Republic of Congo, Côte d’Ivoire, Madagascar and the Gambia. It is noticeable that, in the Republic of Congo (an OPEC member) the collapse of the oil price in 2012-2013 was a major factor in the debt increase that led the country into default with external creditors and face difficult restructuring discussions; however, fraud and corruption were a major factor of fiscal deterioration in other countries such as the Gambia. 30 Although average public debt-to-GDP ratios are more moderate than in Groups 4, 5 and 6, they are also high in some countries (e.g. Cameroon, Egypt, Ghana, Guyana, Jordan, Kyrgyz Republic, Kenya, Malawi, Rwanda, Sri Lanka and Sudan). It is noticeable that in oil exporter countries (e.g., Egypt and Sudan) the fall of the oil price in 2012-2013 was a major driver of debt increase; however, fiscal positions also deteriorated after 2012 in some diversified exporter economies. The factors of declining fiscal positions are quite diverse, and include current spending overruns (e.g. Ghana and Kyrgyz Republic) or spending on major projects (e.g. Cameroon, Kenya and Rwanda). However, China and India (also in Group 7) are among the largest EMs that now issue virtually all their debt in local currency and have become (jointly with Brazil) the dominant source of bilateral financing to LIDC, who have seen a dramatic shift in their creditor base.
16
three European countries: two post-Soviet states (Kazakhstan, an emerging market and oil
exporter, and Kyrgyz Republic, a low-income developing country) and an European Union
country that is classified as an emerging market economy (Poland).
So, all in all, we observe that the effect of a change in the public debt-to-GDP ratio on
GDP growth is lower in developing and emerging market economies (where, in general,
the level of public indebtedness is also lower) than in advanced economies that record the
highest ratios of public debt (see Figure 1)31. However, since the richest countries in the
world do not belong to Group 1 (the ones with the highest effect of a debt change on
economic growth), but to Group 5, there must be other reasons that might explain group
membership. For this reason, in the next section we examine the relevance of the
institutions, the type of expenditure that is funded with debt, the relative level of private
and public indebtedness, and debt maturity in explaining the debt-growth relationship.
Moreover, we investigate whether the heterogeneous impact detected has a different
pattern over time by estimating a new model that allows for specific time-varying slopes
including interactions of the variable itd with the group indicator and year dummies32.
Figure 3 shows the estimated evolution of the coefficient of changes in the public debt-to-
GDP ratio on economic growth by country groups over time. As can be seen, there is
time-varying heterogeneity within and between country groups.
[Insert Figure 3 here]
It can be observed that the more volatile the estimated effect over time (measured by the
standard deviation), the higher the impact. It is quite stable in Groups 6 and 7 and records
the highest volatility in Group 1. It is also noticeable that, in four out of the seven groups
(1, 2, 3 and 5), the negative estimated effect of a debt change on economic growth reaches
its maximum value (in absolute terms) during the period 2010-2012, coinciding with the
Great Recession (2007-2013)33 -the exceptions are Group 4, where the highest estimated
effect takes place in 2006 (before the financial crisis), and Groups 6 and 7 where the
coefficient is quite stable over time-. However, while in Groups 3 and 5 this high negative
effect vanishes very quickly, in Groups 1 and 2 its duration is longer.
31 The gap between the debt of the G20 advanced and emerging market economies is still significant, exceeding 90% of
GDP on average, while low-income developing countries are even clearer outliers, accounting for less than 1% of the
global debt – well below their share of output (see Mbaye et al., 2018). 32 The estimation results are not shown here to save space, but they are available from the authors upon request. 33 According to Eichengreen et al. (2019), about two-thirds of the increase in the advanced-country debt ratio during the Great Recession was accounted for by the cumulative increase in the primary deficit, reflecting revenue losses and expansionary fiscal policies.
17
7. Explaining group membership and time-varying impact
In this section we assess the role of five types of variables as underlying drivers of the
heterogeneous impact of debt on economic growth: (1) the quality of institutions (GQIt),
(2) the composition of public expenditure that is funded with debt (the 10 groups into
which the classification of the functions of government (COFOG) divides government’s
expenditure, see Appendix 4), (3) the relative ratio of private debt indebtedness (DQPRDt),
(4) the relative ratio of public debt indebtedness (DQPDt), and (5) debt maturity (STDt).
With regard to the first variable, the role of sound and efficient institutions in explaining
long-run growth was formalized in a number of contributions in the early 2000s, which
showed that countries with weaker institutions find it harder to sustain growth and are
more vulnerable to experiencing periods of crisis and stagnation34 (see Acemoglu et al.
2001, 2002, 2005a and 2005b). However, the role played by institutions in explaining the
relationship between debt and growth has for the most part been ignored. To the best of
our knowledge, the exceptions are Jalles (2011), Kourtellos et al. (2013), and Kim et al.
(2017)) who find empirical evidence suggesting that the quality of governance, the control
of corruption and the level of democracy are relevant factors influencing the relationship
between debt and economic growth.
Regarding the relationship of expenditure composition and economic growth, there is also
a large body of literature on this issue but, as far as we know, no empirical paper has
examined the effect of the above variables in the debt-growth nexus, in spite of its
relevance. In this connection, Devarajan et al. (1996) and Aschauer (1989) point out that
the impact of public debt on the economy’s performance may depend on whether the
public expenditure funded by government debt is productive or unproductive. While the
former, which includes physical infrastructure (roads and railways), communication,
information systems (phone, internet), education, health-care, and social protection35 may
have a positive impact on the growth rate of the economy, the latter does not affect the
economy’s long-run performance, although it may have positive short-run implications.
34 Good institutions might induce higher investment and therefore lead to sustainable economic growth, and might also reduce uncertainty for economic decision-makers and offer incentives for innovative and productive activities. 35 Although some sort of this investment might not be profitable from the single firm’s point of view (as private costs exceed private returns), the whole economy would nevertheless benefit enormously, which justifies public provision. For instance, Glomm and Ravikumar (1997), among others, contend that both government infrastructure investment and education expenditures have a significant impact on an economy’s long-term growth rate. Afonso and Halles (2014) and Beraldo et al. (2009) show that spending on education and health boosts growth. Finally, Herce et al. (2000, 2001) find a positive growth effect of total social protection expenditure in the European Union.
18
Therefore, the purpose to which debt is put is highly relevant, since while there are good
reasons to issue debt, there have also been political failures that have induced governments
to borrow more than is socially desirable (funding unproductive public expenditure) which
may lead, in some cases, to public debt levels that are hard to justify.
With regard to private debt, we should recall that according to the Global Debt Database
published by the IMF, of the global total debt at the end of 2017 ($184 trillion in nominal
terms, the equivalent of 225% of GDP), only one-third was public debt, the remaining
two-thirds being nonfinancial private debt (debt held by households and nonfinancial
corporations). While the unprecedented increase in public debt and its scale have raised
serious concerns among economists both about its sustainability and about its impact on
economic growth, they have taken a more nuanced position on the risks of private debt
accumulation [Cecchetti et al. (2011), Lombardi et al. (2017) and Gómez-Puig and Sosvilla-
Rivero (2018a) are some of the exceptions]. Nevertheless, all forms of debt, when they are
high and moving upwards, are sources of justifiable concern. In particular, the negative
implications of excessive private debt (a “debt overhang”) for growth and financial stability
are well documented in the literature, underscoring the need for private sector deleveraging
in some countries. In this regard, some authors [see, e.g., Schularick and Taylor (2012) and
Jordà et al. (2016)] demonstrate that high debt levels in the private sector are not only a
good predictor of financial crises, but also a key determinant of the intensity of the ensuing
recession. Moreover, high private debt levels can also hamper growth even in the absence
of a financial crisis, since the accumulation of debt involves risk (International Monetary
Fund, 2016). As debt levels increase, borrowers’ ability to repay becomes progressively
more sensitive to falls in income and sales as well as to increases in interest rates. In fact,
high private debt can have a substantial adverse impact on macroeconomic performance
and stability, as it hinders the ability of households to smooth their consumption, and
affects corporations’ investments. So, as indicated in Section 4, we use yearly data to create
two dummy variables representing our proxies of the relative public and private
indebtedness: (DQPDt) and (DQPRDt), respectively. These dummy variables take values 1
to 4 corresponding to the low indebted, lower middle indebted, upper middle indebted,
and high indebted categories using public and private debt-to-GDP ratios respectively.
Finally, Fatás et al. (2019) stated that one of the reasons why it is difficult to identify
common patterns and to pin down the causal effect of debt on growth is that not all debts
are equal; factors such as debt maturity are key elements that can affect fiscal
19
vulnerabilities and the responses of governments to debt changes. Therefore, as a proxy of
debt maturity, we have introduced short-term debt expressed as percentage of total
external debt (STDt).
In order to assess the effects of the different factors jointly, we run multinomial logit
regressions of the seven estimated groups, using several specifications (see Pindyck and
Rubinfeld, 1998)36. Table 4 presents classification success data for four multinomial logistic
regression models sequentially employing different categories of the selected independent
variables. A look at Table 4 reveals that, except for the indicator of quality of institutions,
the estimated models achieve a high classification success, and are able to render predicted
probabilities that are close to the actual percentage frequency observed in the data.
Therefore, the results suggest that the explanatory variables contain useful information that
allows accurate replication of the country classification generated by the GFE estimation
procedure.
[Insert Table 4 here]
To further analyse the potential determinants of the identified heterogeneous group effects
of public debt variations on growth, we run regressions of the time-varying coefficients of
changes in the public debt-to-GDP ratio on economic growth by country groups (depicted
in Figure 3) on their potential drivers. To overcome the problem of coefficient comparison
when the variables are measured in different units, we use standardized coefficients to
evaluate the relative importance of the different explanatory variables. To this end,
following the proposal of Bring (1994), we use the variance inflation factor to calculate
partial standard deviations that provide standardized coefficients directly related to the
reduction in R2 obtained by excluding the variable from the model37. Table 5 displays the
results.
[Insert Table 5 here]
It can be seen that the variable that captures the quality of the institutions (GQIt) has a
positive significant impact in the relationship between a debt change and growth in five out
of the seven groups (the exceptions being Groups 1 and 4), meaning that, the sounder the
institutions, the less negative or the more positive the effect of a public debt increase on
economic growth. This implies that GQIt has a positive moderating effect on the
36 The results of the multinomial logistic regression estimations are not shown here to save space, but they are available from the authors upon request. 37 See Appendix 6 for further details.
20
relationship between public debt and economic growth, in agreement with Jalles (2011),
Kourtellos et al. (2013), and Kim et al. (2017), who also found empirical evidence that the
quality of governance, the control of corruption and the level of democracy are relevant
factors influencing the relationship between debt and economic growth. The variable that
gauges the relative level of public indebtedness (DQPDt) registers a negative impact in the
debt-growth nexus in four groups of countries (1, 2, 5 and 6). Interestingly, on average, the
relative level of public debt is low in Groups 1 and 2, while it is high in Groups 5 and 6.
These results suggest that the threshold beyond which an increase in public debt has a
negative effect on economic growth differs across countries (see, e.g., Edberhardt and
Presbitero (2015) or Chudik et al. (2017)). Specifically, this threshold is much lower in
countries in Groups 1 and 2 (i.e., the room for manoeuvre for increasing public debt is very
limited, even when their level of public indebtedness is already low) than in Group 5 and 6
countries (where the estimated effect of a debt increase on growth is much lower, although
their level of public indebtedness is considerably higher). As for the relative level of private
indebtedness (DQPRDt) it turns out to have a significant negative impact on the debt-
growth relationship in two groups of countries (2 and 5, which are mainly integrated by
advanced economies, especially Group 5) where the level of private indebtedness is very
high (see Table 2), in line with the results presented by Schularick and Taylor (2012) or
Jordà et al. (2016), among others, who pointed out the negative implications of excessive
private debt for growth and financial stability. Turning to the case of the relationship of
expenditure composition and the debt-growth relationship, our results reinforce the idea
that the impact of a public debt increase on the economy’s performance might depend on
whether the public expenditure funded by government debt is productive or unproductive
[see Aschauer (1989), Devarajan et al. (1996)]. It can be observed that, if public debt funds
unproductive expenditure [GF01t (general public services), GF02t (defence), and GF08t
(recreation, culture and religion)], its impact on economic growth is negative (in four and
five out of seven groups in the case of GF01t and GF08t respectively). However, if
sovereign debt funds expenditure in some of the other seven groups into which
government expenditure is divided according to the classification of the functions of
government (COFOG), the impact on economic growth is positive in some groups of
countries. Specifically, the groups of expenditure where a rise in spending implies a positive
impact on the debt-growth nexus in more groups of countries are: GF04t (economic affairs,
which includes roads, railways, communication, and information systems, and has a
positive effect in five out of the seven groups), GF09t (education, which also has a positive
21
effect in five out of the seven groups of countries), and GF10t (social protection, which
registers a positive impact in six out of the seven groups, the only exception being Group
5, the countries with the highest level of social protection). A rise in expenditure in the
other four groups of public spending only affects the debt-growth nexus positively in two
or three out of the seven groups. In particular, a rise in GF05t (environmental protection,
including sewage system operation) implies a positive impact in the debt-growth
relationship in countries in Groups 1, 6, and 7 (we should recall that Groups 6 and 7
include some of the lowest-income developing countries in our sample), while a rise in
GF03t (public order and security, including law courts), in GF06t (housing and community
amenities) and in GF07t (health) is associated with a positive impact in the debt-growth
nexus in countries in Groups 3 and 5, Groups 2 and 6, and Groups 1 and 4, respectively.
Finally, the higher the proportion of short-term debt, the more negative the impact of an
increase in debt on economic growth in the seven group of countries (the impact being
especially high in Group 4) as pointed out by Fatás et al. (2019).
8. Concluding remarks
In this paper we have used the GFE method proposed by Bonhomme and Manresa (2015)
as opposed to a standard fixed effects estimator to examine whether the debt-growth
relationship might differ substantially across different groups of countries, using a sample
that comprises 116 advanced, emerging and developing economies over the period 1995-
2016. To the best of our knowledge, this is the first paper to apply the GFE methodology
to examine the heterogeneous relationship between public debt and economic growth both
across countries and over time. The GFE accounts for unobserved time-varying
heterogeneity across groups of countries in panel data models, group membership being
estimated along with the other parameters in the model by minimizing the sum of squares
of residuals. Moreover, this paper also contributes to the literature by analysing the drivers
of the heterogeneous impact of debt on economic growth. To that end, we first explore the
determinants of group membership, making use of a multinomial logit regression model to
assess the role of five types of variables: (1) the quality of institutions, (2) the composition
of public expenditure funded with debt, (3) the relative public indebtedness, (4) the relative
private indebtedness, and (5) the maturity of debt. We then analyse the role of these
22
variables in explaining the time-varying impact of public debt on growth in the country
groups identified. Our paper therefore shifts the focus of research on the long-run effects
of ‘‘high levels’’ of public debt towards its interplay with the deep determinants of growth
(institutions and public policies) as the new growth theories have recently proposed (see, e.
g., Capolupo, 2009).
Our findings suggest that the relationship between public debt and growth varies across
countries. In particular, the GFE estimator endogenously splits the sample into seven
groups of countries that have dissimilar time patterns and a different estimated impact of a
debt change on economic growth (ranging from -0.43 in Group 1 to -0.031 in Group 7).
When analysing the heterogeneous time-varying impact of public debt on growth, our
results indicate that the debt-growth relationship is crucially mitigated by the quality of a
country’s institutions and intensified by the level of both public and private indebtedness
and the maturity of debt. The type of expenditure that is funded with debt also influences
that relationship (negatively in the case of unproductive spending, and positively in the case
of productive spending).
Regarding policy implications, our results indicate that the nexus between public debt and
economic growth differs according to country and is crucially related to diversity in
institutions and public policies that make up the socio-economic environment. Therefore,
we consider that our results may have some practical meaning for national policymakers
and international organizations responsible for global economic surveillance, and provide
theoretical insights for academic scholars interested in the identification of growth
determinants and factors responsible for the differences in growth in the data observed.
Funding
This paper is based on work supported by the Spanish Ministry of Economy and
Competitiveness [grant ECO2016-76203-C2-2-P].
23
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26
Appendix 1. The 116 countries included in the sample
Note: The main criteria used by the International Monetary Fund to classify the world into advanced economies, emerging market and developing economies are (1) per capita income level, (2) export diversification — thus, so oil exporters that have high per capita GDP would not make the advanced classification because around 70% of its exports are oil; and (3) degree of integration in the global financial system.
Income group Countries
29 Low income developing countries
(LIDC)
Burkina Faso, Cameroon, Cape Verde, Comoros, Congo Republic, Congo Democratic Republic, Côte d'Ivoire, The Gambia, Ghana, Guinea, Guyana, Haiti, Honduras, Kenya, Kyrgyz Republic, Madagascar, Malawi, Mali, Mauritania, Moldova, Nepal, Nicaragua, Niger, Nigeria, Rwanda, Senegal, Sudan, Tanzania, Uganda.
54 Emerging market economies (EM)
Algeria, Argentina, The Bahamas, Bahrain, Barbados, Belarus, Belize, Bolivia, Botswana, Brazil, Bulgaria, Chile, China, Colombia, Costa Rica, Croatia, Dominican Republic, Ecuador, Egypt, El Salvador, Eswatini, Fiji, Gabon, Guatemala, Hungary, India, Indonesia, Iran, Jamaica, Jordan, Kazakhstan, Malaysia, Mauritius, Mexico, Morocco, Namibia, Oman, Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Romania, Russia, Saudi Arabia, Seychelles, South Africa, Sri Lanka, Thailand, Tunisia, Turkey, Ukraine, Uruguay.
33 Advanced economies (AE)
Austria, Belgium, Canada, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Iceland, Ireland, Israel, Italy, Japan, Korea Republic, Latvia, Lithuania, Luxembourg, Malta, The Netherlands, New Zealand, Norway, Portugal, Singapore, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, United Kingdom, United States.
Appendix 2: Definition of the explanatory variables and data sources
Variable Description Source
Real growth rate (gt) Growth rate of real per capita GDP (annual %) World Development Indicators (World Bank)
Level of Output (yt) Per capita Gross domestic product at 2010 market prices World Development Indicators (World Bank)
Public debt-to-GDP ratio (dt) Ratio of public debt to GDP World Development Indicators (World Bank)
Population growth (POPGRt) Population growth (annual %) World Development Indicators (World Bank)
GCF-to-GDP ratio (GCFt) Ratio of gross capital formation to GDP (%) World Development Indicators (World Bank)
Openness (OPENt) Absolute sum of exports and imports over GDP World Development Indicators (World Bank)
Inflation (INFt) Inflation as measured by the consumer price index (annual %)
World Development Indicators (World Bank),
Appendix 3
Variable Description Source
(GQIt) This is an average of the value of the following four indicators, rescaled in order that it lies between zero and one.
Government effectiveness
(GEt)
Reflects perceptions of the quality of public services, the quality of the civil service and the degree of its independence from political pressures, the quality of policy formulation and implementation, and the credibility of the government’s commitment to such policies.
The Worldwide Governance
Indicators (World Bank)
Regulatory Quality (RQt)
Reflects perceptions of the ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development.
The Worldwide Governance
Indicators (World Bank)
Rule of law
(RLt)
Reflects perceptions of the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence.
The Worldwide Governance
Indicators
(World Bank)
Control of corruption
(CCt)
Reflects perceptions of the extent to which public power is exercised for private gain, including both petty and grand forms of corruption, as well as “capture” of the state by elites and private interests.
The Worldwide Governance Indicators
(World Bank)
(DQPDt) Dummy variable that takes values
1 to 4 corresponding to low, low-middle,
upper-middle, and high indebted
countries
Public Debt-to-GDP
(PUBDEBTt or dt)
Ratio of public debt over GDP
World Development Indicators
(World Bank)
(DQPRDt)
Dummy variable that takes values
1 to 4 corresponding to low, low-middle,
upper-middle, and high indebted
countries
Private Debt-to-GDP
(PRDEBTt)
This variable is calculated as the sum
of two components: (1) bank loans to domestic households and nonfinancial corporations, drawn from the IMF’s Standardized Reporting Forms (SRFs) and International Financial Statistics (IFS) and (2) the outstanding stock of debt securities issued (on the domestic and international markets) by non-financial corporations, calculated based on securities issuance data from Dealogic database. Data are in percentage of GDP.
Global Debt Database (International Monetary
Fund)
(STDt) Debt maturity
Short term debt expressed as percentage of total external debt.
World Development Indicators (World Bank) and
Coordinated Portfolio Investment Survey, CPIS
(IMF)
29
Appendix 4
Note: Expenditure in the different COFOG is presented as percent of GDP.
Variable Description Source
General Public Services (GF01t)
Executive and legislative organs, financial and fiscal affairs, external affairs; foreign economic aid; general services; basic research; R&D related to general public services; general public services not else classified (n.e.c.); public debt transactions, transfers of a general character between different levels of government.
Government Financial Statistics (International Monetary Fund)
Defence (GF02t)
Military defence; civil defence; foreign military aid, R&D related to defence; defence n.e.c.
Government Financial Statistics (International Monetary Fund)
Public order and
safety (GF03t)
Police services; fire-protection services; law courts; prisons; R&D related to public order and safety; public order and safety n.e.c.
Government Financial Statistics (International Monetary Fund)
Economic affairs
(GF04t)
General economic, commercial and labour affairs; agriculture, forestry; fishing and hunting; fuel and energy; mining, manufacturing and construction; transport; communication; other industries, R&D related to economic affairs; economic affairs n.e.c.
Government Financial Statistics (International Monetary Fund)
Environment
protection (GF05t)
Waste management; water waste management; pollution abatement; protection of biodiversity and landscape; R&D related to environmental protection.
Government Financial Statistics (International Monetary Fund)
Housing and
community amenities (GF06t)
Housing development; community development; water supply; street lighting; R&D related to housing and community amenities; housing and community amenities n.e.c.
Government Financial Statistics (International Monetary Fund)
Health (GF07t)
Medical products, appliances and equipment; outpatient services; hospital services; public health services; R&D related to health; health n.e.c.
Government Financial Statistics (International Monetary Fund)
Recreation, culture
and religion (GF08t)
Recreational and sporting services; cultural services; broadcasting and publishing services; religious and other community services, R&D related to recreation, culture and religion; recreation; culture and religion n.e.c.
Government Financial Statistics (International Monetary Fund)
Education
(GF09t)
Pre-primary, primary, secondary and tertiary education, post-secondary non-tertiary education, education non definable by level, subsidiary services to education, R&D; n.e.c.
Government Financial Statistics (International Monetary Fund)
Social protection
(GF10t)
Sickness and disability; old age; survivors; family and children; unemployment; housing; R&D; social protection and social exclusion n.e.c.
Government Financial Statistics (International Monetary Fund)
30
Appendix 5. Brief description of the GFE estimator
The GFE estimation introduces time-varying grouped patterns of heterogeneity in linear
panel data models important to establish whether the relationship under study is
heterogeneous across groups of countries. The estimator minimizes a least squares
criterion with respect to all possible groupings of the cross-sectional units. The most
appealing feature of this approach is that group membership is left unrestricted. The
estimator is suitable for N big and T small and it is consistent, since both dimensions of
the panel tend to infinity.
One of the most common approaches to model unobserved heterogeneity in panel data is
the use of time-invariant fixed-effects. This standard approach is sometimes subject to
poorly estimated elasticities when there are errors in the data or when the explanatory
variables vary slowly over time. Moreover, it is restrictive in that unobserved heterogeneity
is assumed to be constant over time. The GFE introduces clustered time patterns of
unobserved heterogeneity that are common within groups of countries. Both the group-
specific time patterns and group membership are estimated from the data. The relationship
between observed variables and the unobserved group heterogeneity is unrestricted,
allowing for the existence of correlations that would create omitted variable bias in
standard fixed-effects estimates.
Our benchmark specification is a linear model that explains economic growth, git, with
grouped patterns of heterogeneity and takes the form:
𝑙𝑛 𝑔𝑖𝑡 = 𝑥𝑖𝑡′ 𝛽 + 𝛾𝑔𝑖𝑡 + 𝑢𝑖𝑡 (A5.1)
where 𝑥𝑖𝑡′ are the covariates that are assumed to be contemporaneously uncorrelated with
the error term, 𝑢𝑖𝑡 , but are allowed to be arbitrarily correlated with group-specific
unobserved heterogeneity, 𝛾𝑔𝑖𝑡. The countries in the same group share the same time
profile and the number of groups is to be decided or estimated by the researcher and group
membership remains constant over time.
In essence, countries that have similar time profiles of growth – net of the explanatory
variables – are grouped together. The main underlying assumption is that group
membership remains constant over time.
31
The model can be easily modified to allow for additive time-invariant fixed effects, which is
our preferred specification38. We apply the within transformation to the dependent and
independent variables and estimate the model with variables in deviations with respect to
the within-mean. The new transformed variables are denoted as 𝑥𝑖𝑡̈ = (𝑥𝑖𝑡 −
�̅�𝑖) 𝑎𝑛𝑑 �̈�𝑖𝑡 = (𝑔𝑖𝑡 − �̅�𝑖), 𝑒𝑡𝑐.
The GFE in model (A5.1) is the outcome of the minimization of the following expression:
(�̂�, 𝛾, �̂�) = 𝑎𝑟𝑔𝑚𝑖𝑛(𝛽,𝛾,𝛼) ∈Θ×𝐴𝐺𝑇×Γ𝐺
∑ ∑ (�̈�𝑖𝑡𝑇𝑡=1
𝑁𝑖=1 − �̈�𝑖𝑡
′ 𝛽 − �̈�𝑔𝑖𝑡)2
(A5.2)
where the minimum is taken over all possible groupings α={g1,…,gn} of the N units into
groups, common parameters 𝛽 and group-specific time effects 𝛾.
An alternative characterization, which is based on concentrated group membership
variables, is introduced for computational purposes. Then, the optimal group assignment
for each country is given by:
�̂�𝑖(𝛽, 𝛾) = 𝑎𝑟𝑔𝑚𝑖𝑛𝑔𝜖{1,…,𝐺}
∑ (�̈�𝑖𝑡𝑇𝑡=1 − �̈�𝑖𝑡
′ 𝛽 − �̈�𝑔𝑖𝑡)2
(A5.3)
where the minimum g is chosen in case of a non-unique solution. The GFE estimator of
beta and gamma could be expressed as:
(�̂�, 𝛾) = 𝑎𝑟𝑔𝑚𝑖𝑛(𝛽,𝛾) ∈Θ×𝐴𝐺𝑇
∑ ∑ (�̈�𝑖𝑡𝑇𝑡=1
𝑁𝑖=1 − �̈�𝑖𝑡
′ 𝛽 − �̈��̂�𝑖(𝛽,𝛾)𝑡)2
(A5.4)
where the GFE estimate of gi is �̂�𝑖(�̂�, 𝛾) and the group probabilities are unrestricted and
individual-specific.
There are two algorithms available to minimize expression (A5.4). The first one uses a
simple iterative strategy and is suitable for small-scale datasets, whereas the second, which
exploits recent advances in data clustering, is preferred for larger-scale problems. The
former is used in this paper39.
38 The idea is to control not only for time-variant group-specific heterogeneity, but also for time-invariant country-specific unobserved heterogeneity. 39 Very similar results were obtained using the second procedure.
32
Appendix 6. Brief description of Bring (1994)’s new standardize regression coefficients.
Consider an estimated regression equation of y on x1, x2,…, xk:
1 1 2 2`... k ky x x x (A6.1)
Traditional standardized regression coefficients can be calculated by first standardizing all
variables,
*
*
, 1,...,i ii
i
y
x xx i k
s
y yy
s
(A6.2)
where ix and y are the means of each variable in the sample and is and ys are the
standard deviations, and then estimate( A6.1) by ordinary least squares with the
standardized variables, being the regression coefficients in this equation the standardized
regression coefficients.
The standardized coefficients are interpreted as the standard deviation change in the
dependent variable when the independent variable is changed by one standard deviation,
holding all other variables constant. Therefore, instead of comparing changes by one unit
as in the usual regression coefficients, the comparison is between changes of standard
deviations.
Bring (1994) proposes an alternative way to calculate consistent standardized coefficients
using the variance inflation factor (VIF). In this way, when y is regressed on x1, x2,…, xk
each independent variable is associated with a VIF:
* ( 1) / ( )ii
i
ss n n k
VIF (A6.3)
Bring (1994) shows although the traditional standardized coefficient is not directly related
to the reduction in R2 obtained by excluding the variable from the model, the new
standardized coefficients are. The reduction in R2 is larger when a variable with a larger
coefficient is removed compared with the loss if a variable with a smaller coefficient is
removed. Therefore, Bring (1994)’ proposal is helpful in measuring the relative importance
of a given explanatory variable. Indeed, as Afifi and Clarke (1990) contend, a variable's
33
standardized coefficient is related to the variable's contribution to the prediction of y, and
the more a variable contributes to the prediction of Y, the more important it is.
34
Figure 1: Government debt-to-GDP
Note: The sample includes 116 countries divided by the International Monetary Fund into advanced, emerging market and low-income developing economies according to: (1) per capita income level, (2) export diversification, and (3) degree of integration into the global financial system.
0.0
20.0
40.0
60.0
80.0
100.0
120.0
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Government Debt-to-GDP: 1995-2016
Advanced Economies Emerging Markets Low-Income Developing Countries
Figure 2: Impact of changes in public debt on economic growth by groups of countries
© GeoNames, HERE, MSFT, Microsoft, NavInfo, WikipediaCon tecnología de Bing
1 4 7Impact of debt on economic growth
36
Figure 3: Time-varying coefficients of changes in the public debt-to-GDP ratio on economic growth.
-2
-1.5
-1
-0.5
0
0.5
1
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7
37
Table 1: Parameter estimates for the benchmark model
OLS FE GFE
1tg 0.290***
(0.027)
0.190***
(0.018)
0.286***
(0.034)
td -0.093**
(0.011)
-0.078***
(0.007)
-0.072**
(0.011)
tHK 0.155
(0.180)
0.167
(0.163)
0.343*
(0.169)
tOPEN 0.050***
(0.010)
0.005
(0.007)
0.003
(0.008)
tINF -0.007**
(0.003)
-0.011***
(0.002)
-0.008**
(0.003)
tPOPGR -0.407***
(0.058)
-0.755***
(0.108)
-0.651***
(0.065)
tGCF 0.075***
(0.010)
0.113***
(0.012)
0.075***
(0.012)
Constant 0.163
(0.252)
1.035**
(0.300)
2.112*** (0.823)
Country FE No Yes No
Group FE No No Yes
Year FE No Yes Yes
Group-year FE No No Yes
Time trend Yes No No
N 2435 2435 2435
Adjusted R2 0.265 0.265 0.544
BIC 12242.68 11753.10 11746.57
RMSE 2.961 2.675 2.331
Notes: The table reports estimated coefficients from the basic empirical model and its extension to exploring the possibility of heterogeneous effects, given by equations (2) and (4) respectively. OLS, FE and GFE denote, respectively, results from pooled-OLS, fixed-effects and grouped fixed effect estimation methods. The dependent variable is gt , the growth rate of real per capita GDP. Δdti is variation in the public debt-to-GDP ratio, ΔHKt is the variation of human capital, ΔOPENt is the variation in openness to trade, INFt is the GDP deflator inflation rate, POPGRt is the population growth rate and GCFt is the ratio of gross capital formation to GDP. Robust standard errors in brackets. GFE results obtained with algorithm 1, described in Appendix 5. *** p<0.01, ** p<0.05, * p<0.1
38
Table 2: Composition of detected groups ordered according to the debt coefficient
GROUP 1: Region Income group
Other classifications Public indebtedness
Private indebtedness
Estonia Europe & Central Asia AE OECD; EMU LI HI
Latvia Europe & Central Asia AE OECD; EMU LI LMI
Lithuania Europe & Central Asia AE EMU LI UMI
Ukraine Europe & Central Asia EM LMI UMI
GROUP 2: Region Income group
Other classifications Public indebtedness
Private indebtedness
Korea, Rep. East Asia & Pacific AE G20; OECD LI HI
Singapore East Asia & Pacific AE HI HI
Indonesia East Asia & Pacific EM G20; Oil Exporter LI LMI
Malaysia East Asia & Pacific EM UMI HI
Thailand East Asia & Pacific EM LMI HMI
Russia Europe & Central Asia EM G20; Oil Exporter LI UMI
Botswana Sub-Saharan Africa EM LI LI
GROUP 3: Region Income group
Other classifications Public indebtedness
Private indebtedness
Moldova Europe & Central Asia LIDC LMI LI
Belarus Europe & Central Asia EM LI
Turkey Europe & Central Asia EM G20; OECD LMI LMI
Romania Europe & Central Asia EM EU LI LMI
Bulgaria Europe & Central Asia EM EU LI UMI
Slovak Rep. Europe & Central Asia AE OECD; EMU LMI UMI
Brazil Latin America & Caribbean EM G20 HMI HMI
Argentina Latin America & Caribbean EM G20 LMI LMI
Chile Latin America & Caribbean EM OECD LI UMI
Colombia Latin America & Caribbean EM LMI LMI
Ecuador Latin America & Caribbean EM OPEC UMI LMI
Panama Latin America & Caribbean EM UMI
Paraguay Latin America & Caribbean EM LI LMI
Peru Latin America & Caribbean EM LMI LMI
Honduras Latin America & Caribbean LIDC UMI LMI
Namibia Sub-Saharan Africa EM LI
GROUP 4: Region Income group
Other classifications Public indebtedness
Private indebtedness
Ireland Europe & Central Asia AE OECD; EMU HI HI
Luxembourg Europe & Central Asia AE OECD; EMU LI HI
Malta Middle East & North Africa AE EMU UMI HI
Dominican Rep.
Latin America & Caribbean EM LI LMI
Seychelles Sub-Saharan Africa EM HI
Cape Verde Sub-Saharan Africa LIDC HI LMI
GROUP 5: Region Income Other classifications Public Private
39
group indebtedness indebtedness
Austria Europe & Central Asia AE OECD; EMU UMI HI
Belgium Europe & Central Asia AE OECD; EMU HI HI
Cyprus Europe & Central Asia AE EMU UMI HI
Finland Europe & Central Asia AE OECD; EMU LMI HI
France Europe & Central Asia AE G20; OECD; EMU LMI HI
Germany Europe & Central Asia AE G20; OECD; EMU UMI UMI
Greece Europe & Central Asia AE OECD; EMU HI UMI
Italy Europe & Central Asia AE G20; OECD; EMU HI UMI
Netherlands Europe & Central Asia AE OECD; EMU UMI HI
Portugal Europe & Central Asia AE OECD; EMU UMI HI
Slovenia Europe & Central Asia AE EMU LI UMI
Spain Europe & Central Asia AE OECD; EMU UMI HI
Czech Rep. Europe & Central Asia AE OECD; EU LI UMI
Denmark Europe & Central Asia AE OECD; EU LMI HI
Sweden Europe & Central Asia AE OECD; EU LMI HI United Kingdom Europe & Central Asia AE G20; OECD; EU LMI HI
Croatia Europe & Central Asia EM EU LMI UMI
Hungary Europe & Central Asia EM OECD; EU UMI UMI
Iceland Europe & Central Asia AE OECD LMI HI
Norway Europe & Central Asia AE OECD; Oil Exporter LMI HI
Switzerland Europe & Central Asia AE OECD UMI HI
Canada North America AE G20; OECD HI HI
United States North America AE G20; OECD UMI HI
Japan East Asia & Pacific AE G20; OECD HI HI
New Zealand East Asia & Pacific AE OECD LMI HI
Fiji East Asia & Pacific EM LMI
Bahamas Latin America & Caribbean EM LI HI
Barbados Latin America & Caribbean EM HI
Belize Latin America & Caribbean EM HI
El Salvador Latin America & Caribbean EM LMI LMI
Jamaica Latin America & Caribbean EM HI UMI
Mexico Latin America & Caribbean EM G20; OECD; Oil Exporter LMI LMI
Nicaragua Latin America & Caribbean LIDC HI LMI
Haiti Latin America & Caribbean LIDC LMI LI
Israel Middle East & North Africa AE OECD UMI UMI
Algeria Middle East & North Africa EM OPEC LI LI
Iran Middle East & North Africa EM OPEC LI LMI
South Africa Sub-Saharan Africa EM G20 LMI UMI
Comoros Sub-Saharan Africa LIDC HI LI
Mauritania Sub-Saharan Africa LIDC HI LMI
GROUP 6: Region Income group
Other classifications Public indebtedness
Private indebtedness
Congo Rep. Sub-Saharan Africa LIDC OPEC HI LI
Congo, D.R. Sub-Saharan Africa LIDC HI LI
Côte d'Ivoire Sub-Saharan Africa LIDC HI LI
Gambia Sub-Saharan Africa LIDC UMI LI
Madagascar Sub-Saharan Africa LIDC UMI LI
Mali Sub-Saharan Africa LIDC LMI LI
Niger Sub-Saharan Africa LIDC HI LI
Gabon Sub-Saharan Africa EM OPEC UMI
Morocco Middle East & North Africa EM UMI UMI
Oman Middle East & North Africa EM Oil Exporter LI UMI
Saudi Arabia Middle East & North Africa EM G20; OPEC LI LMI
Nepal South Asia LIDC UMI LMI
40
GROUP 7: Region Income group
Other classifications Public indebtedness
Private indebtedness
Burkina Faso Sub-Saharan Africa LIDC LMI LI
Cameroon Sub-Saharan Africa LIDC Oil Exporter HI LI
Ghana Sub-Saharan Africa LIDC UMI LI
Guinea Sub-Saharan Africa LIDC UMI LI
Kenya Sub-Saharan Africa LIDC UMI LMI
Malawi Sub-Saharan Africa LIDC UMI LI
Nigeria Sub-Saharan Africa LIDC OPEC LI LI
Rwanda Sub-Saharan Africa LIDC HI LI
Sudan Sub-Saharan Africa LIDC Oil Exporter HI LI
Tanzania Sub-Saharan Africa LIDC LMI LI
Uganda Sub-Saharan Africa LIDC UMI LI
Eswatini Sub-Saharan Africa EM LI
Mauritius Sub-Saharan Africa EM UMI UMI
Senegal Sub-Saharan Africa EM LI LI
Bahrain Middle East & North Africa EM LI UMI
Egypt Middle East & North Africa EM Oil Exporter HI LMI
Jordan Middle East & North Africa EM HI UMI
Tunisia Middle East & North Africa EM UMI
Bolivia Latin America & Caribbean EM Oil Exporter LMI
Costa Rica Latin America & Caribbean EM LMI LMI
Guatemala Latin America & Caribbean EM LI LMI
Uruguay Latin America & Caribbean EM UMI LMI
Guyana Latin America & Caribbean LIDC HI LMI
India South Asia EM G20 UMI LMI
Pakistan South Asia EM UMI LMI
Sri Lanka South Asia EM HI LMI
China East Asia & Pacific EM G20 LI UMI
Philippines East Asia & Pacific EM UMI LMI
Kazakhstan Europe & Central Asia EM Oil Exporter LI LMI
Kyrgyz Europe & Central Asia LIDC HI LI
Poland Europe & Central Asia EM OECD; EU LMI LMI
Note: Regarding income groups, for operational and analytical purposes, economies are divided among three groups according to the International Monetary Fund (IMF) classification. Therefore, AE, EM and LIDC stand for Advanced Economies, Emerging Market Economies and Low-Income Developing countries. The main criteria used by the IMF to classify the world into advanced economies, emerging market and developing economies are (1) per capita income level, (2) export diversification— so oil exporters that have high per capita GDP would not make the advanced classification because around 70% of its exports are oil; and (3) degree of integration into the global financial system. As for other classifications: OECD: Organisation for Economic Cooperation and Development; EU: European Union; EMU: European Economic and Monetary Union; OPEC: Organization of the Petroleum Exporting Countries; G20: Group of twenty economies that account for around 90% of the gross world product. In relation to relative public and private indebtedness, based on public and private debt-to-GDP ratios, we have classified them as low indebted (LI), lower middle indebted (LMI), upper middle indebted (UMI), and high indebted (HI), the cut-off points between each of the groups being the first, the second and the third quartiles.
41
Table 3: Heterogeneous effects by groups, GFE
Notes:
The table reports estimated coefficients from the extended model to explore the possibility of heterogeneous effects,
given by equation (4), including interactions of the variable Δdt with the group indicator variables.
The dependent variable is gt, the growth rate of real per capita GDP. Δdt is variation in the public debt-to-GDP ratio,
ΔHKt is the variation of human capital, ΔOPENt is the variation in openness to trade, INFt is the GDP deflator inflation
rate, POPGRt is the population growth rate and GCFt is the ratio of gross capital formation to GDP.
Group 1, Group 2, …, Group 7 are dummy variables that take the value 1 if the country belongs to the corresponding
group or zero otherwise. Table 2 lists the countries in each group.
Robust standard errors in round brackets. Regression includes group FE, year FE and group-year FE.
*** p<0.01, ** p<0.05, * p<0.1
GFE
1tg 0.173***
(0.018)
Group1* td -0.430***
(0.050)
Group 2* td -0.227***
(0.041)
Group 3* td -0.143*** (0.016)
Group 4* td -0.113***
(0.019)
Group 5* td -0.092***
(0.015)
Group 6* td -0.035***
(0.012)
Group 7* td -0.031***
(0.022)
tHK -0.034 (0.160)
tOPEN 0.008
(0.007)
tINF -0.011***
(0.002)
tPOPGR -0.738***
(0.011)
tGCF 0.106***
(0.012)
Constant 1.199*** (0.383)
N 2435
42
Table 4: Explaining group membership
Observed Frequency
Predicted frequencies
Quality of
institutions
Composition
of public
expenditure
Relative
public and
private
indebtedness
Debt maturity
Group 1 3.41 5.23 3.40 3.39 3.39
Group 2 6.03 4.62 6.03 6.06 6.03
Group 3 13.79 12.58 13.77 13.81 13.77
Group 4 5.18 6.48 5.12 5.19 5.12
Group 5 34.49 41.94 34.62 34.49 34.63
Group 6 10.34 10.77 10.33 10.33 10.32
Group 7 26.76 17.72 26.73 26.73 26.74
Note:
The table reports the observed frequency and the predicted frequencies generated by multinomial logit regression using
the different set of independent variables: second column uses a government quality indicator (GQI); third column uses
expenditure on general public services (GF01); expenditure on defence (GF02); expenditure on public order and safety
(GF03); expenditure on economic affairs (GF04); expenditure on environment protection (GF05); expenditure on
housing and community amenities (GF06); expenditure on health (GF07); expenditure on recreation, culture and religion
(GF08); expenditure on education (GF09); and expenditure on social protection (GF010); fourth column uses relative
public and private indebtedness (DQPD and DQPRD, respectively); and the final column uses a proxy the short-term debt
(STD).
See Table 2 for the list of countries belonging to each group.
43
Table 5: Exploring drivers of time-varying coefficients by groups Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7
GQI 0.0629 (3.2214)
5.9607** (2.7343)
1.4718** (0.6814)
0.3112 (0.4932)
0.6206** (0.2758)
0.7374*** (0.2269)
0.9234** (0.4312)
DQPD -0.2021* (0.1135)
-1.1454** (0.5206)
-0.5845 (1.0486)
-0.5072 (0.3503)
-0.4727** (0.2055)
-1.1531*** (0.3631)
-0.0183 (0.4658)
DQPRD -0.3127 (0.7802)
-2.1802** (0.9955)
-0.5880 (0.4827)
-0.6903 (1.2634)
-0.1201** (0.0529)
-1.6800 (1.1079)
-0.4812 (0.3436)
GF01 -1.0025** (0.4516)
-0.5533** (0.2586)
-0.9937 (0.7920)
-0.3437 (0.4127)
-0.4155*** (0.1323)
-0.5382 (05174)
-0.0629** (0.0294)
GF02 -0.7625 (0.6333)
-2.2672 (2.2278)
-0.9030 (0.6231)
-0.3434 (0.4263)
-0.2844 (0.5974)
-1.5507 (4.9610)
-0.5223** (0.2396)
GF03 0.6838 (0.8313)
2.3398 (1.7400)
0.9353*** (0.2960)
-0.3180 (0.9615)
0.4865*** (0.1484)
0.5233 (0.7981)
0.2421 (0.3396)
GF04 0.1472** (0.0660)
0.4156 (0.7592)
0.1894*** (0.0608)
0.0484 (0.1613)
0.0436*** (0.0141)
0.9651*** (0.2797)
0.7772** (0.3533)
GF05 0.1481*** (0.0467)
0.1161 (0.6504)
0.1549 (1.1355)
0.3036 (0.3014)
0.2130 (0.3450)
0.0652*** (0.0188)
0.2400*** (0.0755)
GF06 0.2010 (0.5710)
0.5610*** (0.1645)
0.7055 (0.7102)
0.2368 (0.4750)
0.3957 (1.0877)
0.8469** (0.3884)
0.3440 (0.3678)
GF07 0.3868** (0.1719)
0.3300 (0.8984)
0.5767 (1.3004)
0.9875** (0.4631)
0.0854 (0.3647)
0.0863 (0.5086)
0.6741 (0.8329)
GF08 -1.10329*** (0.3415)
-0.3509 (1.2218)
-0.3831** (0.1821)
-1.0951*** (0.4081)
-0.6840** (0.3095)
-5.1393*** (1.4080)
-0.7481 (0.8070)
GF09 1.8264*** (0.5854)
0.2727** (0.1151)
0.4180 (0.7344)
0.2655 (0.4506)
0.0973** (0.0447)
0.7887** (0.3585)
0.2121*** (0.0682)
GF010 1.0632** (0.4968)
4.7131*** (1.5204)
1.1983*** (0.4996)
0.4091** (0.1853)
1.0266 (0.6267)
1.2388*** (0.3570)
0.6746*** (0.2213)
STD -1.2967*** (0.4027)
-0.8266** (0.3723)
-1.4838** (0.6901)
-5.7101*** (2.2687)
-0.1532*** (0.0483)
-0.3310*** (0.1006)
-0.0854*** (0.0276)
Constant -0.5777** (0.2697)
-1.1810*** (0.3650)
-0.6644*** (0.2741)
-0.4775** (0.2211)
-0.0.2811*** (0.0940)
-3.6936** (1.6563)
-0.2609*** (0.0803)
Adjusted R2 0.6782 0.6735 0.6888 0.6145 0.6410 0.6964 0.6687
RMSE 2.1813 2.646 1.8470 4.1703 3.9491 3.7511 3.4540
44
Notes: The table reports estimated coefficients from a regression of the time-varying slopes by groups depicted in Figure 3 on its postulated determinants. GQI is a government quality indicator; DQPD and DQPRD are relative public and private indebtedness, respectively; GF01 denotes expenditure on general public services; GF02 denotes expenditure on defence; GF03 denotes expenditure on public order and safety; GF04 denotes expenditure on economic affairs; GF05 denotes expenditure on environment protection; GF06 denotes expenditure on housing and community amenities; GF07 denotes expenditure on health; GF08 denotes expenditure on recreation, culture and religion; GF09 denotes expenditure on education; GF10 denotes expenditure on social protection; and STD is a proxy the short-term debt. See Table 2 for the list of countries belonging to each group. Robust standard errors in round brackets. *** p<0.01, ** p<0.05, * p<0.1. The bold letters show the statistically significant coefficients.
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